This invention relates to geophysical exploration for petroleum and minerals. More particularly, this invention is directed to geophysical prospecting by means of the seismic technique, whereby mechanical or seismic energy is imparted to the earth and the resulting seismic wave which propagates through the earth is reflected at the interfaces of different subsurface geological formations, the seismic reflections are detected, and the seismic reflection data are later processed in order to map the subsurface geological structure. Specifically, this invention is directed to methods and apparatus for analyzing the seismic data in cases where a vibrator is used for imparting seismic energy to the earth, commonly referred to in the field to which this invention relates as "Vibroseis.RTM.".
In the Vibroseis.RTM. geophysical exploration technique, a frequency modulated signal is employed as the source of seismic energy. This signal is commonly referred to as a sweep and for most operations is modulated such that its instantaneous frequency is a linear function of time. The electrical signal or pilot which establishes the oscillations in the vibrator's driving element is routinely recorded for later processing steps.
Ideally, each receiver on the surface of the earth records seismic data consisting of two components: (1) the convolution of the sweep signal with the earth's impulse response and (2) additive noise. The resulting seismic data are usually referred to as an uncorrelated trace. In accordance with the conventional processing technique, the traces from each receiver are cross-correlated with the pilot. See N. A. Anstey, "Correlation Techniques-A Review", Geophys. Prosp., v. 12, pp. 355-382, 1964. The resulting outputs are referred to as correlated traces. Seismic reflection events are then determined from the correlated traces, just as they would be determined from an impulsive source trace.
The Vibroseis.RTM. geophysical exploration technique is similar in principle to chirp radar systems. See J. R. Klauder, A. C. Price and S. Darlington, "The Theory and Design of Chirp Radars", Bell Syst. Tech. J., v. 25, pp. 261-278, 1960. A low power, long duration signal is used as the system input. Input pulse compression is then achieved by correlating the received signal with the input pulse. Correlating the seismic data with the pilot is equivalent to filtering the seismic signal with a digital matched filter, where the impulse response of the matched filter is the pilot reversed in time and delayed so that it is causal. In the presence of additive white noise, this would be the optimum detection procedure (in an instantaneous signal-to-noise-ratio sense) for the case in which adjacent reflection events are separated in time by at least twice the duration of the pilot. However, because the reflection events are not restricted in their separation and because the matched filtering or correlation is performed digitally after sampling, the result is suboptimal.
Two difficulties arise when one attempts to resolve reflection events from correlated data. If the original reflection event can be represented by a discrete impulse, that event will be much broader in time after the correlation process. The impulse is replaced by the autocorrelation function of the pilot, the Klauder wavelet. Because of the bandwidth limitation imposed by the sweep limits, there is a loss of resolution in the process. This is also true in impulsive source exploration. The second problem concerns interactions between proximate reflection events. The correlation process will reproduce Klauder wavelets centered at each event. Oscillations in the tails of these wavelets will tend to obscure other reflection events. This problem is compounded by the tendency of reflection events to decay in magnitude with time. Due to the length of the pilot autocorrelation function, even reflection events occurring much later in time can be totally masked by correlation effects from earlier events. It is desirable then that an approach be developed which would improve resolution of the reflection events.